The image-based depiction of surfaces of a tubular object that has a complicated shape and possibly many branches, such as e.g. the bronchial system, a blood vessel system or other hollow organs, forms the basis for a multiplicity of analyses, particularly in the clinical field. For example, a wide diversity of problems can be identified by means of a virtual ‘fly-through’ through the hollow organ, the simulation of a liquid flow, or the detailed three-dimensional depiction of critical regions, such that further action can be effectively established in relation to the medical treatment in particular. This presupposes the availability of preferably complete information relating to the topological structure of the tubular object. Such information relating to the topological structure can be obtained e.g. by way of imaging methods such as computer tomography or magnetic resonance tomography, for example. Without further processing, the images and depictions thus obtained are not suitable or are only partly suitable for the cited analyses. The multidimensional description of the surface of the hollow organ by means of a boundary surface network depiction or a surface network model, subsequently referred to simply as a ‘boundary surface network’, provides the desired geometric information and is moreover intended also to express sufficient details of the surface for the cited analyses.
Methods for calculating a boundary surface network of a hollow organ in accurate detail, describing the surface by way of numerically complicated and computationally intensive interpolations, are known. The calculated boundary surface networks are generally characterized by excellent accuracy of detail. However, as a result of the huge computing effort involved, these depictions cannot be calculated at short notice or instantaneously, and therefore realtime manipulation, e.g. for the purpose of ‘what-if’ analyses (e.g. in order to simulate the insertion of a stent in a blood vessel), is only partly possible using these methods for calculating the boundary surface network.
The required speed in the determination of the boundary surface network can be achieved e.g. by simplifying the numerical effort by using the simplest possible model of the surface. In contrast with ‘model-free’ interpolation calculation methods based on the analysis of point clouds, such models use a set of simple geometric shapes such as e.g. cylinders or spheres to approximate the hollow organ that is to be reproduced. However, this approximation only rarely produces a boundary surface network of the hollow organ in which critical details are expressed with a sufficient degree of accuracy, particularly in the region of branch points. Consequently, these methods are unsuitable for precisely measuring geometric changes of the vascular system for the purpose of diagnosis and planned treatment of a pathology.
For the purpose of simulating a liquid flow, for example, the complete geometry and in particular the branches of the hollow organ must be expressed in a manner that is as far as possible identical to nature, further to which the calculated boundary surface network must often be ‘waterproof’, i.e. there must not be any openings that are not present in reality.
These requirements are only rarely satisfied by results from the model-based determination of a boundary surface network, however, since in particular the adaptation of the simple geometric basic shape is complicated if the size ratios of partial structures of the hollow organ vary significantly and if branches occur, for example. In particular, unwanted artifacts in the determined boundary surface network occur at branches because geometric basic model elements (e.g. spheres) that are often used for modeling project into each other, for example, and structures that are not present in reality are modeled in the interior of the determined boundary surface network. These boundary surface networks are only of limited use for the cited ‘fly-through’ applications, for example.